Don't try to race it, plan for a bit of extra time to get there. Wear less clothing.
In Melbourne these days I wear a shirt with windproof polarfleece sleeveless vest over it, trousers and
maybe windproof gloves on the colder days. Yes I ride in work clothing - no facilities for changing/storing clothes or shower at the workplace. I would be dressed a fair bit warmer if I was out on a morning touring ride. It is a bit cold for the first km, but the first hill soon warms me up
In winter cold weather, wear merino base layers - it wicks sweat away and doesn't build up a stink. For summer try to get some high-wicking travel shirts.
Try to ride a bit easier for the last 2 kms of your commute.
Remember - sweat is basically water, except for from the armpits and nether regions which contains a lot of body oil. A wipe and deodoriser will do wondes there. Also it really takes 12-24 hrs for sweat to begin to pong. Modern urban man and woman has a real fetish for
clean that is unwarranted.
Riding bikes in traffic - what seems dangerous is usually safe; what seems safe is often more dangerous.